# Len invests $5200 at 6% per annum simple interestÂ & Harpeeet invests $3600 at 6% p.a compounded quarterly. When will Harpreet's investment be worth more than Len's.

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### 1 Answer

Let the number of years after which the investment of Harpreet and Len will be the same be N.

As Len invested $5200 at 6% p.a. simple interest, after N years it is worth 5200(1 + N*0.06)

Harpreet invested $3600 at 6% p.a. compounded quarterly, after N years it increases to 3600*(1.015)^(4*N)

Equating the two and solving for N

5200(1 + N*0.06) = 3600*(1.015)^(4*N)

The equation can only be solved using trial and error. Using the same, the value of the right hand side is more than the left hand side after 19 years.

**Harpreet's investment is worth more than Len's after 19 years.**